Evaluate `intsqrt((1-x)/(1+x))dx`.

Explanation

We have `intsqrt((1-x)/(1+x))dx=int{(sqrt(1-x))/(sqrt(1+x))xx(sqrt(1-x))/(sqrt(1-x))}dx`
`=int((1-x))/(sqrt(1-x^(2)))dx=int(dx)/(sqrt(1-x^(2)))-int(x)/(sqrt(1-x^(2)))dx`
`=sin^(-1)x+(1)/(2)*int((-2x))/(sqrt(1-x^(2)))dx`
`=sin^(-1)x+(1)/(2)int(dt)/(sqrt(t)), "where" (1-x^(2))=t and (-2x)dx = dt`
`=sin^(-1)x+(1)/(2)intt^(-1//2)dt=sin^(-1)x+(1)/(2)*(t^(1//2))/((1//2))+C`
`=sin^(-1)x+sqrt(1-x^(2))+C`.
Integrals of the form `int(dx)/(sqrt((ax^(2)+bx+c)))`.
Method Put `(ax^(2)+bx+c)` in the form ` a{(x+alpha)^(2)+-beta^(2)}` and then integrate.